TeXipedia

xrightharpoondown

Draws a right-pointing harpoon with a downward-oriented barb above mathematical expressions.

Overview

Commonly employed in advanced mathematics and physics to denote specialized mappings or transformations with specific directional properties.

  • Often used in category theory and abstract algebra to indicate particular types of morphisms.
  • Appears in texts discussing vector fields and differential geometry.
  • Useful for representing specialized mathematical operations where both direction and orientation are significant.
  • Frequently combined with other arrow notations to create precise mathematical notation systems.

Examples

Representing a vector transformation with downward mapping.

vTwv \xrightharpoondown{T} w
v \xrightharpoondown{T} w

Indicating a decreasing limit or convergence from above.

xnnxx_n \xrightharpoondown{n \to \infty} x
x_n \xrightharpoondown{n \to \infty} x